What are the solutions to the equation x^3-9x^2+21x-5=0 ?

The solutions to the equation x^3-9x^2+21x-5=0 are x=5,x=2+sqrt(3),x=2-sqrt(3)

Find the zeros of x^3-9x^2+21x-5=0

The zeros of x^3-9x^2+21x-5=0 are x=5,x=2+sqrt(3),x=2-sqrt(3)

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x^{3} - 9 x^{2} + 21 x - 5 = 0

x = 5, x = 2 + 3, x = 2 - 3

Decimal

x = 5, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x^{3} - 9 x^{2} + 21 x - 5 = 0

Factor

x^{3} - 9 x^{2} + 21 x - 5 : (x - 5) (x^{2} - 4 x + 1)

(x - 5) (x^{2} - 4 x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{2} - 4 x + 1 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

The solutions are

x = 5, x = 2 + 3, x = 2 - 3

200 x - 0.02 x^{2} - 0.000002 x^{3} - 80000 = 0

(1 + 12 x^{2})^{3} = 0

2 x^{3} - 14 x^{2} + 2 x - 14 = 0

24 x^{3} + 46 x^{2} + 9 x - 9 = 0

r^{4} + 6 r^{3} + 17 r^{2} + 22 r + 14 = 0

What are the solutions to the equation x^3-9x^2+21x-5=0 ?
The solutions to the equation x^3-9x^2+21x-5=0 are x=5,x=2+sqrt(3),x=2-sqrt(3)
Find the zeros of x^3-9x^2+21x-5=0
The zeros of x^3-9x^2+21x-5=0 are x=5,x=2+sqrt(3),x=2-sqrt(3)